Power steering system frequency suppressor

ABSTRACT

A frequency suppressor for a hydraulic system is shown and described. The frequency suppressor comprises a housing that contains a substantially fixed mass of a compressible substance. The volume of the compressible substance is varied to dampen frequency disturbances in the hydraulic system.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application is a divisional of U.S. patent application Ser.No. 11/410,596, filed Apr. 25, 2006, the entirety of which is herebyincorporated by reference, and claims the benefit of U.S. ProvisionalApplication No. 60/753,086, filed on Dec. 22, 2005, the entirety ofwhich is hereby incorporated by reference.

FIELD

Fluid driven actuation devices are disclosed, wherein fluid pumped atelevated pressure effects actuation, and in particular to thesuppression and/or damping of fluid pressure disturbances, which maymanifest themselves as audible noise or tangible vibrations.

BACKGROUND

In hydraulic systems, even with a fully filled fluid circuit, normaloperation may create pressure disturbances within the fluid of subsecond duration and/or frequency. Fluid disturbance effects may beconsidered as falling into two general categories. For example, in powersteering hydraulic systems, a first fluid disturbance effect may beconsidered as relating to vehicle reliability insofar as disturbancesmay build to a resonance and/or impose stresses on components that couldlead to premature component failure and/or loss of vehicle control. Asecond fluid disturbance effect may be considered as relating tonuisance insofar as the disturbance gives rise to noises and/orvibrations noticeable to the vehicle occupants. “Reliability”disturbances indiscernible by the occupants may thus not constitute anuisance as such, just as “nuisance” disturbances may not affect thereliability of the vehicle. Notwithstanding the apparent inconsequentialnature of “nuisance” disturbances, they are of significant importance tovehicle manufacturers insofar as they have profound effects on customersatisfaction with the product.

It will be appreciated that whether or not a physical disturbance effectis considered as noise or a vibration depends upon its frequencyrelationship to the physiologically defined senses of any occupant oruser; in physical terms both are vibrations and are hereinafterconsidered as such except when specifically distinguished. Such varietyof disturbances which affect, that is, are noticeable to, the occupantsof motor vehicles are also often called by the collective term “noise,vibration, harshness” or its abbreviation “NVH”.

Moreover, these issues are not limited to a fluid actuation device inthe form of a vehicle steering mechanism for which the fluid is ahydraulic liquid. Analogous fluid driven actuation devices for nonvehicular use and/or devices using gaseous driving fluid may suffer someor all of the outlined effects and benefit from an alternative approachto damping.

SUMMARY OF THE EMBODIMENTS

A frequency suppressor comprises a housing having an interior and aplurality of internal chambers within the interior. The frequencysuppressor also comprises a substantially fixed mass of a compressiblesubstance contained in the housing, wherein the substantially fixed massof the compressible substance occupies a volume that varies in responseto pressure fluctuations in the hydraulic system. In certain exemplaryembodiments, the housing has a length and the plurality of internalchambers is spaced apart along its length. In other exemplaryembodiments, the housing has at least one separator disposed along itslength within the interior, such that the housing and the separatordefine the plurality of internal chambers. In still other exemplaryembodiments, the separator comprises an orifice. In further exemplaryembodiments, the plurality of internal chambers comprises a firstinternal chamber in fluid communication with a second internal chamber,the housing has a separator disposed along its length within theinterior, such that the housing and the separator define the first andsecond internal chambers, a first portion of the substantially fixedmass of the compressible substance is contained in the first internalchamber, a second portion of the substantially fixed mass of thecompressible substance is contained in the second internal chamber, andwhen the hydraulic system pressure fluctuates, there is a pressure dropacross the separator.

A hydraulic system for delivering a liquid comprises a pump having adischarge connected to a discharge conduit, and a substantially fixedmass of a compressible substance in fluid communication with liquidcontained in the discharge conduit. The substantially fixed mass of thecompressible substance occupies a volume that varies in response topressure fluctuations in the hydraulic system.

A method of suppressing frequency disturbances in a hydraulic system isprovided. The method comprises providing a substantially fixed mass of acompressible substance and varying the volume of the compressiblesubstance to dampen the frequency disturbances.

BRIEF DESCRIPTION OF THE DRAWINGS

Embodiments of the invention will now be described by way of example ingreater detail with reference to the attached figures, in which:

FIG. 1 shows the general arrangement of a vehicle fluid power assistedsteering system incorporating a frequency suppressor.

FIG. 2 is a cross-sectional view of the frequency suppressor of FIG. 1.

FIG. 3 is a graph depicting the noise suppression characteristics of anembodiment of a frequency suppressor, as illustrated with a test vehiclepower steering system.

FIG. 4 is a graph depicting the relative noise suppressioncharacteristics of an embodiment of a frequency suppressor and a knowndevice.

DETAILED DESCRIPTION

FIG. 1 shows generally at 200 a fluid driven actuation device comprisinga power assisted steering system of a road vehicle (not shown) in whichit is mounted. Although the specific system of FIG. 1 is a powersteering system, embodiments may be used with other types of hydraulicsystems, and their use is not limited to power steering applications norto systems having hydraulic liquid. For example, gaseous driving fluidmay also benefit. As will be explained in greater detail below, powersteering system 200 includes frequency suppressor 44 which utilizes afixed mass of a compressible substance to dampen and/or suppressfrequency disturbances.

In the power assisted steering system of FIG. 1, fluid in the form ofhydraulic oil under pressure is used to reduce the steering effort forthe vehicle driver. The power assisted steering system comprises anactuator in the form of a rack 20 mounted on the body or chassis thereofcoupled to the road wheels by track rods 22 and 24 and within casing 26gearing (not shown) at a pressure determined by the turn angle of thesteering wheel coupling the track rods to a steering wheel 28. Thesecomponents comprise a mechanical circuit of the device.

The steering system also comprises a pump 30 driven by the vehicle primemover (e.g., an internal combustion engine or separate electric motor);the manner of driving power assisted pumps for various systems withinvehicles is well known and not described further. Output from the pumpdischarge is taken by way of a supply line 32 to a steering gear valve34 of the device mounted by the rack casing. Steering gear valve 34applies high pressure liquid to a rack piston (not shown) to supplementforce applied by the driver to the steering wheel. Return line 36connects a rigid conduit 37 on steering gear valve 34 to reservoir 38.Suction line 39 connects reservoir 38 and pump 30. The components 30 to39 comprise a hydraulic circuit of the device.

Insofar as the reservoir is typically at atmospheric pressure, thendepending upon the flow of liquid around the system, the pump creates apressure rise of from slightly below to significantly above atmosphericpressure and the fluid, in passing through the steering gear valve andrack actuator, suffers a pressure drop such that although the fluidleaving the rack is above atmospheric pressure, it is low in relation tothe pump delivery pressure and further diminishes as a pressure gradientalong the return line to the reservoir.

As indicated in FIG. 1, pump 30 is connected to a generally rigiddischarge conduit 40, which is connected to one end of hose 32.Discharge conduit 40 comprises a branched structure such as a “y” or“t,” and in the embodiment of FIG. 1 includes a branch 41 for attachingadditional hydraulic system components. Hose 32 is generally flexiblealong its length and is connected at one end to a rigid conduit 35 atsteering gear valve 34.

The pump may create fluid disturbances in the form of high pressurepeaks and other effects due to cavitation within the pump, whichdisturbances may emanate from the high pressure part of the hydrauliccircuit and/or have influence on the actuator and return line parts.Furthermore, the steering gear valve 34 may be the source of mechanicalnoises and pressure disturbances within the fluid. Within the steeringarrangement of a road vehicle, the turning force needed from thesteering wheel increases as a function of the increase in angle of theroad wheels from the straight ahead position; in supplying fluid powerassistance from the hydraulic circuit this is effected by designing thesteering gear valve with a so called boost curve that provides littlepower assistance for large increments to small absolute turning angles,but large gains in assistance for small incremental changes at largeabsolute angles. Such a large gain, and thus sensitivity to smallchanges, applies both to commanded inputs from the steering wheel andinvoluntary disturbances resulting from external shocks transmitted intothe system from the road wheels. Insofar as the valve typically hasinternal components displaced in accordance with pressure differentialsto define fluid flow orifices, it is possible at high gain for suchinternal components to succumb to oscillation or flutter, amplifyingvariations in fluid pressure and creating mechanical noise. It is alsopossible for such valve to create noise and flow disturbances due topassage of fluid through small orifices therein, and for such noise andflow disturbances to pass from the steering gear valve through the lowpressure return line. Such noises derived from the steering gear valveare sometimes referred to as “rack rattle” and “grunt”. Such disturbancetends to be at lower frequencies than pump cavitation noises in the highpressure line.

In accordance with a first embodiment of the invention, there isprovided a frequency suppressor within the steering system, beingindicated generally at 44. As used herein, the term “suppressor” shouldbe understood to encompass frequency dampening devices which reduce theeffects (e.g., noise) caused by frequency disturbances, and the term isnot limited solely to devices that completely eliminate their effects.

The frequency suppressor is coupled to discharge conduit 40 of pump 30,preferably as close to the pump discharge as possible. In the embodimentof FIG. 1, suppressor 40 is attached to branch 41 on discharge conduit40. Although frequency suppressor 40 could be located on return line 36,or farther downstream from discharge conduit 40, it is believed thatlocating it as close as possible to the pump discharge beneficiallydampens pump frequency disturbances before they affect the steeringgear.

The hydraulic circuit of power steering system 200 is a closed system.Any compressible substance, such as air or other compressible gas,contained in suppressor 44 will generally remain therein, save forrelatively minor amounts which may dissolve in the hydraulic oil. As aresult, frequency suppressor 44 provides a substantially fixed mass of acompressible substance which is in fluid communication with thehydraulic oil discharged from pump 30.

The compressible substance occupies a volume within suppressor housing45 (shown in FIG. 2) which varies in response to pressure changes in thehydraulic oil, thereby dampening and/or suppressing them. For example,as the hydraulic oil discharge pressure increases, the level of oil insuppressor 44 will rise to compress the compressible substance, therebyexpanding the liquid volume of system 200 and at least partiallyoffsetting the pressure increase. Conversely, as the hydraulic oildischarge pressure decreases, the level of oil in suppressor 44 willdecrease, allowing the compressible substance to expand, thereby atleast partially offsetting the pressure decrease. Thus, frequencysuppressor 44 effectively provides a variable surge volume for systemfrequency disturbances.

In power steering systems such as system 200, hydraulic oil is used toactuate a rack piston. In contrast, the compressible substance referredto herein is not used as an actuating fluid, but rather, provides avariable surge volume for the hydraulic oil. As indicated above,hydraulic fluids used in accordance with the foregoing embodiments aregenerally incompressible, and the compressible substance used insuppressor 44 is generally significantly compressible. However, knownfluids vary as to their specific viscosities, and the particularsubstances selected for the compressible substance and hydraulic oil mayaffect the frequency suppression response of suppressor 44. As thecompressible substance becomes relatively more compressible than thehydraulic oil, suppressor 44 will tend to suppress frequencydisturbances more quickly and/or more completely because changes in theliquid volume within housing interior 45 of suppressor 44 will morequickly change the volume of the compressible substance in housinginterior 45. As the relative compressibility of the compressiblesubstance and hydraulic oil decreases, the opposite effect will occur.

Referring to FIG. 2, a preferred embodiment of frequency suppressor 44is depicted. Frequency suppressor 44 may have a variety of differentshapes. However, for ease of manufacturing and to evenly distributestresses throughout housing 45, it is preferably symmetrical. In theembodiment of FIG. 2, frequency suppressor 44 comprises a generallycylindrical housing 45 with a partially-spherical, solid closed end 60.Nevertheless, other shapes such as spherical shape or a symmetricalpolygonal shape could also be used.

A compressible substance, preferably a compressible gas such as air, iscontained within the interior of housing 45. The interior preferablycomprises a plurality of internal chambers. In the embodiment of FIG. 2,two internal chambers 46 and 48 are provided. As described furtherbelow, the use of a plurality of internal chambers minimizes the amountof hydraulic fluid entering chamber 48. This helps prevent the hydraulicoil from becoming entrained in or mixing with the compressiblesubstance, which could diminish compressibility, and consequently, thedamping ability of suppressor 44. To further prevent the mixing ofhydraulic oil and the compressible substance, frequency suppressor 44 ispreferably installed in an upright position with respect to the ground(see FIG. 1). Because the hydraulic oil has a relatively greater densitythan the compressible substance, an upright orientation further reducesthe likelihood that the hydraulic oil will mix with or become entrainedin the compressible substance.

Separator 50 is provided to separate the interior of housing 45 intochambers 46 and 48. Separator 50 may comprise a number of differentshapes and geometries, but is preferably designed to prevent mixing ofthe compressible substance from the hydraulic oil. In the embodiment ofFIG. 2, separator 50 is an orifice with a single through-hole 52.However, it may also include a plurality of openings.

It is believed that the opening area of separator 50 affects thesensitivity of suppressor 44 to pressure fluctuations. Referring to FIG.2, if the compressible substance/hydraulic oil interface is located inchamber 46, as the hydraulic oil pressure increases, the interface willmove to the left (towards chamber 48), forcing a portion of thecompressible substance into chamber 48, and increasing the mass of thecompressible substance contained in the chamber's fixed volume. It isbelieved that some of the force applied to the compressible substance bythe hydraulic oil will dissipate across separator 52 causing a temporarypressure drop across separator 52 due to its restricted opening area.Because of this dissipation, the pressure in chamber 48 will not respondimmediately to changes in the pressure in chamber 46, but instead, willexperience a slight delay and/or lagged response. Conversely, as thehydraulic oil pressure decreases, the compressible substance/hydraulicoil interface will move to the right, allowing some portion of thecompressible substance to enter chamber 46, decreasing the mass of thecompressible substance contained in the fixed volume of chamber 48 whileincreasing the mass of the compressible substance contained in the fixedvolume of chamber 46. However, the opening area of separator 50 willcause a delay and/or lag in the expansion of compressible substance intochamber 48. Thus, it is believed that the restricted opening area ofseparator 50 will effectively filter the response of the compressiblesubstance pressure in chamber 48 to changes in hydraulic oil pressure inchamber 46.

As suggested by the foregoing, it is believed that by adjusting therelative opening area (e.g., the area of orifice hole 52) of separator50, suppressor 44 can be “tuned” to obtain the desired response ofsuppressor 44 to hydraulic system pressure changes. However, as theopening area increases, the likelihood of entraining hydraulic oil inthe compressible substance also increases. Thus, the opening area (e.g.,the area of the orifice hole 52) of separator 50 is preferably sized tobe about eight (8) to about twelve (12) percent of the interiorcross-sectional area (i.e., the area perpendicular to the length ofhousing 45). However, opening areas of from about nine (9) to abouteleven (11) percent of the cross-sectional area are more preferred andan opening area of about ten (10) percent of the cross-sectional area isespecially preferred. In one exemplary embodiment of suppressor 44,chambers 46 and 48 are cylindrical and have a diameter of about eight(8) mm, while separator 50 comprises a 2.5 mm thick orifice with a hole52 diameter of about 2.5 mm.

The ratio of the volumes of chambers 46 and 48 may also affect thedamping performance of suppressor 44. For ease of manufacturing, thevolumes are substantially equal. However, ratios of 30 percent to about70 percent (volume of chamber 46/volume of chamber 48) may also be used.In one exemplary embodiment, chambers 46 and 48 each have a diameter ofabout 8 mm and a length of about 38 mm.

Suppressor 44 also preferably provides mass damping to dissipate fluiddisturbances in hydraulic system 200. To obtain mass damping without theuse of an unduly large suppressor 44, relatively dense materials such assteel or aluminum are preferred. In exemplary embodiments, the ratio ofthe mass of suppressor 44 to its internal volume (i.e., fluid volume) isgenerally from about 8 to about 16 g/cm³. Ratios of from about 10 toabout 12 g/cm³ are preferred and a ratio of 11.5 g/cm³ is especiallypreferred. In one exemplary embodiment, suppressor 44 has a mass of 44 gand an internal fluid volume of about 3.8 cm³.

Referring again to FIG. 2, suppressor 44 is generally shaped tofacilitate attachment to hydraulic system 200. Tapered neck 54 andhexagonal fitting 56 are provided to facilitate attachment with a wrenchor pliers. Male threaded connector 58 is provided to allow forengagement with a threaded female connector in branch 41 of conduit 40.Conversely, connector 58 may be designed as a female connector thatengages a male connector on hydraulic system 200. Other known connectorsmay also be used. Unlike many known devices used for frequencysuppression, suppressor 44 may be readily installed on an existing powersteering system without performing extensive modifications to it.

Typical hydraulic systems operate at pressures up to about 2000 psi.Thus, suppressor 44 should be designed to reliably withstand thesepressures. In the embodiment of FIG. 2, housing 45 generally has a wallthickness t of from about 40 percent to about 60 percent of the innerdiameter d of housing 45. Thicknesses of from about 45 to about 55percent of the inner diameter are preferred and a thickness of about 50percent is especially preferred. In one exemplary embodiment, suppressor44 has an inner diameter of about 8 mm and a wall thickness of about 4mm.

Closed end 60 of suppressor 44 is preferably a solid semi-sphericalshape. Closed end 60 has a minor axis x that is generally from about 35to about 45 percent of the outer diameter of suppressor 44. Morepreferably, minor axis x is about 38 percent of the outer diameter. Inone exemplary embodiment, suppressor 44 has an outer diameter of about16 mm and closed end 60 has a minor axis of about 6 mm. Closed end 60also preferably has a solid flange 62 that abuts the interior walls ofhousing 45 within chamber 48. Closed end 60 is preferably a turned partthat is lathed to the desired shape and dimensions. A brazed washer isthen placed between closed end 60 and housing 45. The brazed washer isthen heated such that it melts into place to affix closed end 60 tohousing 45.

The steering system 200 of FIG. 1 is exemplary as regards its mechanicaland hydraulic circuit. Mechanically the described rack may be replacedby a steering box. Furthermore, the hydraulic circuit is one in which apartially filled reservoir defines an atmospheric pressure datum andpermits thermal expansion and contraction of the liquid that maytypically occur with a diurnal cycle. It will be appreciated that theabove described frequency suppressor may be employed in a so calledreservoirless system, wherein the hydraulic circuit is sealed from theatmosphere and includes in the lowest pressure part of the circuit aflexibly walled container that varies its volume to accommodateexpansion and contraction of the enclosed liquid volume without changingthe pressure across its wall.

A method of installing the frequency suppressor 44 will now bedescribed. In accordance with the method, at the time the power steeringsystem is assembled, frequency suppressor 44 is attached to branch 41 ofpump discharge conduit 40 via connector 58. The system is preferablyexposed to the atmosphere before it is charged with hydraulic oil toallow a fixed mass of air to enter the interior of suppressor housing45. The mass will generally equal the inner volume of housing 45 timesthe density of the compressible substance at the prevailing pressure andtemperature. The system is then charged with hydraulic oil, therebytrapping a fixed mass of air in chamber 48. In addition, suppressor 44could also be designed with a valve that allows it to be charged with acompressible substance after installation.

To demonstrate its frequency suppression ability, the suppressor 44 ofFIG. 2 was tested by placing it on a power steering system in a FordFusion test vehicle. Noise data was collected in the cabin of thevehicle as it idled while the steering wheel was rotated from thefully-left rotated position to the fully-right rotated position at agenerally constant rate of rotation. The resulting noise data ispresented in FIG. 3. Referring to FIG. 3, line 72 represents the decibellevel at a reference location in the test vehicle's cabin with nosuppressor connected to the vehicle's power steering system. Line 74represents the decibel level at the same cabin location with suppressor44 attached to the vehicle's power steering system in the mannerdepicted in FIG. 1.

The x-axis in FIG. 3 represents the order of the measured noisefrequency, which is a relative measurement of the cabin noise frequencyas compared to the power steering pump's frequency. The power steeringpump used in the test vehicle was a vane pump having ten (10) vanes. Thevehicle idle speed was 800 RPM. Thus, the disturbance frequencyattributable to the operation of the power steering fluid pump wasapproximately 13.3 rev/second×10 vanes=133 Hz. Both the decibel leveland the frequency of the noise in the test vehicle cabin were recorded.The order numbers on the x-axis of FIG. 3 represent multiples of ten(10) of the frequency of the measured noise divided by the 133 Hz pumpfrequency (i.e. the 10th order corresponds to a 133 Hz noise frequency,the 20th order corresponds to a 266 Hz noise frequency, etc.). As thedata in FIG. 3 indicates, the use of suppressor 44 provided substantialnoise reductions in the test vehicle cabin at the 10th, 20th, 30th, and40th orders. The noise reduction provided by suppressor 44 wasespecially pronounced at the 30th and 40th orders. For example, at the30th order, the unsuppressed noise level was approximately 36 dB whilethe suppressed level was approximately 24 dB.

Next, suppressor 44 was compared to a commercially available noisesuppression device supplied by Dayco Products of Tulsa, Okla. Noise datawas recorded in the vehicle cabin for both devices using the sameprocedure described above with respect to FIG. 3. The resulting noisedata is presented in FIG. 4. The y-axis represents the decibel level inthe test vehicle cabin for both the Dayco device (line 82) andsuppressor 44 (line 84), while the x-axis represents the order of themeasured noise (i.e., the measured noise frequency divided by 133 Hz andmultiplied by 10) for each respective device. As the figure indicates,suppressor 44 provided unexpectedly better noise suppression than theDayco device, especially at the 10th and 20th orders. For example, at a10th order noise frequency, suppressor 44 yielded a decibel level ofapproximately 29 dB while the Dayco device yielded a decibel level of 35dB.

The present invention has been particularly shown and described withreference to the foregoing embodiments, which are merely illustrative ofthe best modes for carrying out the invention. It should be understoodby those skilled in the art that various alternatives to the embodimentsof the invention described herein may be employed in practicing theinvention without departing from the spirit and scope of the inventionas defined in the following claims. It is intended that the followingclaims define the scope of the invention and that the method andapparatus within the scope of these claims and their equivalents becovered thereby. This description of the invention should be understoodto include all novel and non-obvious combinations of elements describedherein, and claims may be presented in this or a later application toany novel and non-obvious combination of these elements. Moreover, theforegoing embodiments are illustrative, and no single feature or elementis essential to all possible combinations that may be claimed in this ora later application.

1. A power steering system, comprising: a power steering wheel assembly;a steering fluid pump for delivering steering fluid to the powersteering wheel assembly; and a substantially fixed mass of acompressible substance in fluid communication with steering fluiddischarged from the pump, wherein the substantially fixed mass of thecompressible substance occupies a volume that varies in response topressure fluctuations in the hydraulic system.
 2. The power steeringsystem of claim 1, further comprising a frequency suppressor, whereinthe pump is connected to a discharge conduit, and the frequencysuppressor is connected to the discharge conduit, the frequencysuppressor comprising (a) a housing having a length and an interiorcontaining the substantially fixed mass of a compressible substance, (b)a plurality of internal chambers within the housing interior, and (c) atleast one separator disposed along the length of the housing within theinterior of the housing, such that the housing and the at least oneseparator define the plurality of internal chambers; wherein one of theplurality of internal chambers contains a substantially fixed volume ofthe compressible substance, and the substantially fixed volume of thecompressible substance has a mass that changes in response to pressurefluctuations in the power steering system.
 3. The power steering systemof claim 2, wherein the steering fluid and the compressible substancedefine an interface within the frequency suppressor.
 4. The powersteering system of claim 1, further comprising a frequency suppressor,the frequency suppressor comprising: a housing having a length, aninterior, and first and second internal chambers within the interior,the first internal chamber being in fluid communication with the secondinternal chamber; a separator disposed along the length of the housingwithin the interior of the housing such that the housing and theseparator define the first and second internal chambers; wherein a firstportion of the substantially fixed mass of the compressible substance iscontained within the first internal chamber, a second portion of thesubstantially fixed mass of the compressible substance is containedwithin the second internal chamber, and when the power steering systempressure fluctuates, there is a pressure drop across the separator. 5.The power steering system of claim 4, wherein the first internal chamberhas a pressure, the second internal chamber has a pressure, and theseparator filters the response of the first internal chamber pressure tochanges in the second internal chamber pressure.
 6. The power steeringsystem of claim 1, further comprising a frequency suppressor, thefrequency suppressor comprising a housing having a length, an interior,and at least one separator disposed along its length within theinterior, wherein the substantially fixed mass of the compressiblesubstance is contained within the housing interior, the housing and theat least one separator define a plurality of internal chambers, and aportion of the compressible substance is displaced from one of theinternal chambers into another of the internal chambers in response topressure fluctuations in the hydraulic system.
 7. The power steeringsystem of claim 6, wherein the housing interior has a cross-sectionalarea, the at least one separator includes at least one opening having across-sectional area, and the opening cross-sectional area is less thanthe housing interior cross-sectional area.